Is the following relation a function? Justify your answer (i) R1 = {(

1.	Is the following relation a function? Justify your answer (i) R1 = {(2, 3), ( 1/2 , 0), (2, 7), (– 4, 6)} (ii) R2 = {(x, \|x \|) \| x is a real number}
Answer» (i) Since (2, 3) and (2, 7) ∈ R₁ ⇒ R₁ (2) = 3 and R₁ (2) = 7 So R₁ (2) does not have a unique image. Thus R₁ is not a function. (ii) R₂ = {(x, \|x \|) / x ∈R} For every x ∈ R there will be unique image as \|x \| ∈ R. Therefore R₂ is a function.

Is the following relation a function? Justify your answer (i) R1 = {(2, 3), ( 1/2 , 0), (2, 7), (– 4, 6)} (ii) R2 = {(x, |x |) | x is a real number}

Answer»

(i) Since (2, 3) and (2, 7) ∈ R₁

⇒ R₁ (2) = 3 and R₁ (2) = 7

So R₁ (2) does not have a unique image. Thus R₁ is not a function.

(ii) R₂ = {(x, |x |) / x ∈R} For every x ∈ R there will be unique image as |x | ∈ R.

Therefore R₂ is a function.